Cellular materials both natural (e.g., wood, cork, trabecular bone) and synthetic (e.g., honeycombs, foams) have superior specific stiffness and strength as well as excellent energy absorption characteristics. When compressed, many of these materials exhibit first a nearly linear elastic regime that is terminated by an instability that leads to localization. Localized deformation is subsequently arrested, triggering its spreading to previously intact neighboring material. This propagation of localized deformation usually progresses with the load remaining nearly, and continues until the whole domain is crushed, in the process tracing an extended load plateau. The relatively low stress levels and extent of such plateaus are responsible for the excellent energy absorption characteristics of these materials. Experimental results from compression tests representative of several families of cellular materials will be used to illustrate this type of behavior, in each case highlighting the governing micromechanical mechanisms. The examples include honeycombs loaded in-plane (2-D crushing) as well as transversely (concertina folding), space-filling polymeric and metallic open cell foams, balsa wood and trabecular bone.